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The dynamic retention of deuterium in a full-tungsten JET-like tokamak is investigated thanks to the Dynamics of Wall Elements (DWE) code. DWE is a wall model coupled to the SolEdge-EIRENE edge-plasma transport code. It is composed of two internal codes: (i) WE-temp, which determines the wall temperature, and (ii) MHIMS, which determines the transport, trapping and desorption of hydrogen isotopes in the wall material. In this work, four consecutive discharges are modeled and analysed with DWE. These discharges are identical and present a transition from a H-mode phase to a L-mode phase, which induces strongly different plasma-wall interactions. The main results are as follows. (i) A release of deuterium is observed at the vicinity of both strike-points at the end of the H-mode phase. This dynamics is explained by an increase of the wall temperature at both strike-points due to the strong plasma heat flux received there, leading to detrapping from trap with low detrapping energy. On the contrary, during the subsequent L-mode phase, the wall temperature at the strike-points decreases, leading to retention by filling the trap emptied during the H-mode. (ii) A release of deuterium from the first-wall is unexpectedly observed at the transition between the H-mode and the L-mode. This release is a consequence of a decrease in implantation energy between the two phases, as it entails a shallower implantation of deuterium. Despite the different material considered in the simulation, the latter result offers a possible explanation of the strong transient release of deuterium experimentally observed in the JET-ILW at the NBI cutoff during high density H-mode discharges.

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International audience; A new neutral fluid code has been developed as a necessary step towards a hybrid fluid/kinetic neutral model, to be used in ITER or DEMO simulations, where part of the divertor will be very collisional for neutrals. The neutral fluid code, which is able to handle complex geometries in view of the coupling to Soledge2D, is tested on plasma backgrounds obtained by Soledge2D‐Eirene in WEST geometry, for different divertor regimes, and is found to be in fair agreement with the kinetic Monte Carlo solver Eirene. The differences are due to the simplifications introduced in the fluid model and to the fact that a fluid description is not fully valid in these cases.

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International audience; The nonlocal expression proposed by Luciani-Mora-Virmont is implemented into a 1D fluid model for the scrape-off layer. Analytic solutions for heat equation are discussed as well as the impact of sheath boundary conditions on the continuity of the temperature profile. The nonlocal heat flux is compared to Spitzer-Härm heat flux for different collisionality.

15th International Workshop on Plasma Edge Theory in Fusion Devices (PET), Nara Kasugano Int Forum IRAKA, Nara, JAPAN, SEP 09-11, 2015; International audience; Cross-field transport in edge tokamak plasmas is known to be dominated by turbulent transport. A dedicated effort has been made to simulate this turbulent transport from first principle models but the numerical cost to run these simulations on the ITER scale remains prohibitive. Edge plasma transport study relies mostly nowadays on so-called transport codes where the turbulent transport is taken into account using effective ad-hoc diffusion coeffecients. In this contribution, we propose to introduce a transport equation for the turbulence intensity in SOLEDGE2D-EIRENE to describe the interchange turbulence properties. Going beyond the empirical diffusive model, this system automatically generates profiles for the turbulent transport and hence reduces the number of degrees of freedom for edge plasma transport codes. We draw inspiration from the k-epsilon model widely used in the neutral fluid community. ((c) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

15th International Workshop on Plasma Edge Theory in Fusion Devices (PET), Nara Kasugano Int Forum IRAKA, Nara, JAPAN, SEP 09-11, 2015; International audience; Power exhaust is one of the major challenges that future devices such as ITER and DEMO will face. Because of the lack of identified scaling parameters, predictions for divertor plasma conditions in these devices have to rely on detailed modelling. Most plasma edge simulations carried out so far rely on transport codes, which most of the times consist of a fluid code for the plasma coupled to a kinetic Monte Carlo (MC) code for neutral particles. One of the main difficulties in interpreting code results is the statistical noise from the MC procedure, which makes it difficult to define a convergence criterion for the simulations. In this work, we elaborate on similarities between noisy transport code simulations and turbulence simulations, and argue that the time averaged solution is a well defined stationary solution for the system. We illustrate these ideas with a simple slab test case with fluid neutrals, to which we add synthetic noise. In this case, the effects of noise are found to be significant only at high noise levels and for large enough correlations times.

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Kinetic Monte Carlo simulations of coupled atom-radiation transport in optically thick divertor plasmas can be computationally very demanding, in particular in ITER relevant conditions or even larger devices, e.g. for power plant divertor studies. At high (∼ 1015 cm–3) atomic densities, it can be shown that sufficiently large divertors behave in certain areas like a black body near the first resonance line of hydrogen (Lyman α). This suggests that, at least in part, the use of continuum model (radiation hydrodynamics) can be sufficiently accurate, while being less time consuming. In this work, we report on the development of a hybrid model devoted to switch automatically between a kinetic and a continuum description according to the plasma conditions. Calculations of the photo-excitation rate in a homogeneous slab are performed as an illustration. The outlined hybrid concept might be also applicable to neutral atom transport, due to mathematical analogy of transport equations for neutrals and radiation.

15th International Workshop on Plasma Edge Theory in Fusion Devices (PET), Nara Kasugano Int Forum IRAKA, Nara, JAPAN, SEP 09-11, 2015; International audience; The impact of a 3D localized particle source on the edge plasma in 3D global turbulence simulations is investigated using the TOKAM3X fluid code. Results apply to advanced fueling methods such as Supersonic Molecular Beam Injection (SMBI) or pellets injection. The fueling source is imposed as a volumetric particle source in the simulations so that the physics leading to the ionization of particles and its localization are not taken into account. As already observed in experiments, the localized particle source strongly perturbs both turbulence and the large scale organization of the edge plasma. The localized increase of the pressure generated by the source drives sonic parallel flows in the plasma, leading to a poloidal redistribution of the particles on the time scale of the source duration. However, the particle deposition also drives localized transverse pressure gradients which impacts the stability of the plasma with respect to interchange processes. The resulting radial transport occurs on a sufficiently fast time scale to compete with the parallel redistribution of particles, leading to immediate radial losses of a significant proportion of the injected particles. Low Field Side (LFS) and High Field Side (HFS) injections exhibit different dynamics due to their interaction with curvature. In particular, HFS particle deposition drives an inward flux leading to differences in the particle deposition efficiency (higher for HFS than LFS). These results demonstrate the importance of taking into account plasma transport in a self-consistent manner when investigating fueling methods. ((c) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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International audience; In recent automated design studies, optimal design methods were introduced to successfully reduce the often excessive heat loads that threaten the divertor target surface. To this end, divertor coils were controlled to improve the magnetic configuration. The divertor performance was then evaluated using a plasma edge transport code and a “vacuum approach” for magnetic field perturbations. Recent integration of a free boundary equilibrium (FBE) solver allows to assess the validity of the vacuum approach. It is found that the absence of plasma response currents significantly limits the accuracy of the vacuum approach. Therefore, the optimal magnetic divertor design procedure is extended to incorporate full FBE solutions. The novel procedure is applied to obtain first results for the new WEST (Tungsten Environment in Steady-state Tokamak) divertor currently under construction in the Tore Supra tokamak at CEA (Commissariat a l’Energie Atomique, France). The sensitivities and the related divertor optimization paths are strongly affected by the extension of the magnetic model

International audience; In this paper we present some investigations of the broadening mechanisms affecting the emission line profiles of impurities present in the divertor regions of tokamaks. For that purpose, we have considered two visible lines (C IV n = 5-6 and n = 6-7) emitted by lithium-like carbon ions for which the contributions of the Zeeman, Stark and Doppler effects are examined. The paper is focused on the impact of differing electron and ion temperatures on the broadening and shapes of the C IV n = 6-7 line for conditions relevant to a detached tokamak divertor plasma. It is shown, that the C IV n = 6-7 line profile calculated with differing electron and ion temperatures may be significantly different from the one calculated with equal temperatures but the same density. This suggests that the electron density determination from the fit of the measured spectra of such a line may be inaccurate when using equal ion and electron temperatures instead of differing ones.

International audience; We present numerical simulations of plasma transport obtained with the SOLEDGE2D code coupled to the EIRENE Montecarlo code for neutrals. We consider a double null magnetic configuration in a WEST geometry. Density and temperatures parallel profiles in the SOL domain are presented as well as Mach profile. We detail how using the penalization technique we are able to model plasma transport up to the first wall having access to energy and particle fluxes on the entire chamber wall. Moreover, we present the computed 2D contour map of the plasma mach number and of the magnitude of the ionisation source term in the whole poloidal section, emphasizing how complex and realistic geometries can be handled thanks to the penalization technique.

12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France); Recent observations of MSE spectra carried out on Tore-Supra show discrepancies between experimental and theoretical intensities calculated at equilibrium. We present here a kinetic model, based on the selectivity of excitation cross sections of Stark states in the parabolic basis. Redistribution due to ion-atom collisions among Stark states of level n=3 allow to calculate the population of Stark states. This model permits to improve significantly the agreement between measured and calculated MSE spectra.

Stark broadening of atomic lines in plasmas is investigated by generating the electric microfield with a renewal process. In this model, the microfield is stepwise constant, with jumping times sampled from a waiting time distribution (WTD). Our model is a true simulation of the renewal process, using random number generators for generating different probability density functions (PDF). The use of an equilibrium static microfield PDF and an exponential waiting time distribution reproduces the so called model microfield method (MMM) results. The work presented is an application to the hydrogen Lyman-α line, for which we compare our renewal process model and ab initio simulations calculations, with the aim of studying the role of non exponential waiting time distributions.

Understanding the mechanisms responsible for the contamination of magnetically confined hydrogen isotope plasmas by impurities is necessary toachieve sustainable and controlled operation of tokamaks. This is especially critical with heavy impurities such as tungsten (W), which are not fully ionized in the plasma core and are thus responsible for potentially large radiative losses. WEST –W Environment in Steady-state Tokamak - is designed to operate long plasma discharges thanks to its super-conducting coils, exposing plasma facingcomponents designed on the technology chosen for ITER. Optimal operation of these components requires to monitor tungsten sources and characterize how eroded tungsten atoms get transported across the scrape off layer into the confined plasma. One of the key questions is to identify the sources driving the contamination, so as to allow scenario optimizations to reduce W ingress in the core. In this work, we rely on spectroscopic measurements in visible and VUV spectral ranges to characterize impurities in WEST plasmas, and useseveral modeling codes (Soledge2D-EIRENE and ERO2.0) to investigate the consistency of available experimental data from various diagnostics (probes, thermocouples, ... ). We make use of spectral line intensities, but also present a detailed study of the line shape of neutral tungsten lines. A Monte Carlo code was specifically developed to simulate how spectral line shape would change with plasma parameters and modeling assumptions. We show that the spectral line shape analysis, when coupled with other diagnostics, can yield information about basic plasma parameters (average incident ion charge, electron and ion temperatures). The model indicates that the line shape is ore sensitive to the change of plasma parameters than the line shift. Together with visible and VUV spectroscopy the parameters obtained from line shape analysis can help constraining the Soledge2D-EIRENE simulations therefore providing more reliable simulation results. However, line shape measurements for tungsten in the visible requires a high resolution spectrometer (with a resolving power of about 400000), which is not currently available on WEST. In order to better understand W contamination pathways, this work presents the first attempts to model WEST plasmas using the ERO2.0 code. The latter uses Soledge2D-EIRENE generated background plasmas as an input, where the radial transport is adjusted so that the plasma background is consistent with available diagnostics. Tungsten transport is then followed kinetically and in the trace approximation on this background allows tofully resolve particle orbits in 3D. This tool allows one to generate poloidal distribution maps of eroded W particles and investigate how different sourceareas (antenna limiter, lower divertor, etc.) influence the poloidal W density field. ERO2.0 simulations were carried out with different wall elements "turned off" as impurity sources, therefore allowing to quantitatively determine the wall element contributing the most for the confined plasma contamination for a given scenario. This was performed for several radial diffusion coefficient values as it is known to significantly change the transport behavior in the scrape off layer. No relevant W line has been observed in the available VUV spectra, but molybdenum can be used as a proxy for W transport analysis. ERO2.0 calculations show a qualitative agreement with the experimental information on the location of Mo4+ emissions in the plasma., Afin d'assurer un fonctionnement contrôlé des tokamaks, il est nécessaire de comprendre les mécanismes responsables de la contamination du plasma confiné d'isotopes d'hydrogène par des impuretés. Ceci est particulièrement critique pour les impuretés lourdes telles que le tungstène (W), qui ne sont pas entièrement ionisées dans le coeur du plasma et peuvent donc être responsables de pertes radiatives importantes. WEST - W Environment in Steady-state Tokamak - est conçu pour produire des décharges longues, et exposer à ces décharges des composants de paroi de technologie identique à celle choisie pour ITER. Le fonctionnement optimal des décharges exige de surveiller les sources de tungstène et de caractériser comment les atomes de tungstène érodés sont transportés à travers les zones périphériques du plasma jusqu'au plasma confiné. L'une des questions clés est d'identifier les sources dominant la contamination, afin de permettre l'optimisation des scénarios pour réduire la quantité de tungstène présente dans le coeur. Dans ce travail, nous nous appuyons sur des mesures spectroscopiques dans les gammes spectrales visible et VUV pour caractériser les impuretés dans les plasmas de WEST, et utilisons plusieurs codes de modélisation (Soledge2DEIRENE et ERO2.0) pour étudier la cohérence des données expérimentales disponibles, provenant de divers diagnostics (sondes, thermocouples, ...). Nous utilisons l'intensité des raies, mais nous présentons également une étude détaillée des profils de raies de tungstène neutre. Un code Monte Carlo a été spécifiquement développé pour simuler ces profils de raies et mettre en évidence les effets des paramètres du plasma et des hypothèses de modélisation. Nous montrons que l'analyse spectrale des profils de raies, couplée à d'autres diagnostics, peut fournir des informations sur la charge ionique incidentemoyenne, et sur les températures ionique et électronique. La forme de la raie est plus sensible à des changements des paramètres plasma que le déplacement du centre de la raie. Les paramètres obtenus à partir de l'analyse de la forme de raie permettent de contraindre d'avantage les simulations Soledge2D-EIRENE et donc de fournir des résultats plus fiables. Cependant, la mesure du profil de raie du tungstène neutre dans le visible nécessite un spectromètre à haute résolution (avec un pouvoir de résolution d'environ 400 000), qui n'est pas disponible actuellement sur WEST. Afin de mieux comprendre les voies de contamination sur WEST, ce travail présente les premières modélisations à l'aide du code ERO2.0. Ce dernier utilise le plasma de fond généré par Soledge2D-EIRENE comme entrée, où le transport radial est ajusté de sorte que ce plasma calculé soit compatible avec les diagnostics disponibles. Le transport du tungstène est ensuite calculé dans une approche cinétique et dans l'approximation d'impureté trace, sur ce plasma de fond, en résolvant les trajectoires des particules en 3D. Cet outil permet de générer des cartes de distribution des particules de W érodées et d'étudier comment différents éléments de paroi (limiteur d'antenne, divertor bas, etc.) contribuent au champ de densité de W. Les simulations ERO2.0 ont été réalisées avec différents éléments de paroi "désactivés" en tant que sources d'impuretés, permettant ainsi de déterminer quantitativement l'élément de paroi contribuant le plus à la contamination du plasma confiné pour un scénario donné. Ceci a été effectué pour plusieurs valeurs du coefficient de diffusion radiale, car ce dernier est mal connu et peut changer de manière significative le transport dans les couches externes du plasma. Aucune raie du W pertinente n'a pu être observée dans les spectres VUV disponibles sur WEST, mais le molybdène peut être utilisé en première approximation pour l'analyse du transport du W. Les calculs ERO2.0 sont en accord qualitatifs avec les informations expérimentales disponibles sur la localisation de l'émission de l'ion Mo4+ dans le plasma.

Magnetic confinement fusion is currently the most advanced way to produce energy thanks to Deuterium/Tritium thermonuclear fusion. One of the challenges is the limitation of the reaction contamination because of Tungsten (W), a material capable of resisting high heat fluxes. W large atomic number causes W to radiate inside tokamak plasmas. If W accumulates in the central part, it cools down the plasma. It is therefore crucial to understand the mechanisms of W transport and identify the actuators of the accumulation process. W transport is involved in complex interplays with many plasma parameters (density, temperature, rotation). Therefore the use of integrated modeling is mandatory in order to evolve self-consistently all those parameters for several confinement times. For the first time, an integrated modeling tool is coupled to first-principles transport codes to self-consistently simulate the time evolution of the W behavior, as well as the evolution of density, temperature, rotation profiles, radiation and external heating. For numerical reasons, several phenomena are not modeled, and the physics of the interaction with the inner wall is simplified. At each time step, this simulation successfully reproduces experimental profiles (density, temperature and rotation), the W central accumulation. Moreover, actuators of the central W accumulation (rotation and central particle fueling) were identified. Finally, integrated modeling simulation allowed bringing out a very interesting non-linear mechanism: the stabilizing effect of W on turbulence. This work demonstrates that first-principles integrated modeling now allows designing and optimizing in advance plasma scenarios with limited W central accumulation., La fusion par confinement magnétique est actuellement la voie la plus avancée pour faire de la fusion thermonucléaire Deutérium/Tritium une source d’énergie exploitable. L’un des défis à relever pour y parvenir consiste à limiter la contamination de la réaction de fusion par le Tungstène (W), un matériau permettant par ailleurs de résister aux hauts flux de chaleur. Le grand nombre atomique du W fait qu'il rayonne dans les plasmas de tokamak. S’il s’accumule au cœur du tokamak, il refroidit le plasma. Il est donc crucial de comprendre les mécanismes du transport du W et d’identifier les paramètres favorisant son accumulation. Le transport du W est intrinsèquement lié aux différents paramètres du plasma (densité, température, rotation) à travers des interactions non-linéaires. La simulation intégrée est le seul outil permettant à tous ces paramètres d’être simulés de manière auto-consistante sur un intervalle de temps de l’ordre de plusieurs temps de confinement. Pour la première fois, l’outil de modélisation intégrée a été couplé à des codes de transport premiers principes pour modéliser de façon auto-consistante les transports turbulent et collisionnel du W, ainsi que l’évolution des profils de densité, température, rotation et radiation, de même que l’évolution du chauffage. Pour des raisons de temps de calcul, certains phénomènes ne sont pas modélisés et la physique de l'interaction avec la paroi interne est simplifiée. A chaque pas de temps, cette simulation reproduit avec succès les signaux expérimentaux (densité, température, rotation) et le comportement du W. De plus, des paramètres physiques responsables de l’accumulation du W (la rotation et la source centrale de particules) ont pu être identifiés. Enfin, la simulation intégrée a permis de mettre en lumière l’effet stabilisant du W sur la turbulence. Grâce à ce travail, nous avons montré que la modélisation intégrée premiers principes permet désormais d'optimiser à l'avance les scénarios de plasma afin d'y limiter l'accumulation de W.